Essentially, Instagram says it had to completely change the way it serves videos in the Android app. With the 15-second cap, the app would download the full video in the background before playing. Now that videos can be up to a minute in length, however, that method would result in some unsavory wait times. To combat this, Instagram says that it switched to a proxy method that allows the video file to be downloaded and played at the same time. This has a number of benefits, Instagram says, but the two that stick out the most are:

Playback is no longer blocked by the video download, i.e. it plays as soon as there's enough content.

Playback is no longer dependent on disk space. Even if the disk cache malfunctions, it would just be treated as a cache miss and streamed directly from the server.

In real terms, Instagram says that it has observed that videos start 20-25% faster with the new system compared to the old. If you're into learning all of the technical hooks behind the process, be sure to check out Instagram's full blog post for much more.